Options Guide

This article describes the basics of Quedex options. We also recommend reading:

OPTION PAYOFFS & P/L

Quedex offers european vanilla options and, same as in the futures contracts, inverse notation is used, which means that the outcome of the contract is as follows

(#) Option Payoff (BTC) = Side * max[ Type * (1 / Strike Price - 1 / Settlement Price), 0]

where:

  • Side - 1 for long position and -1 for short position,
  • Type - 1 for a call option and -1 for put option,
  • Settlement Price - price in dollars of 1 BTC at which the position is closed,
  • Strike Price - price in dollars at which the option may be exercised at expiration.

Example - put option

Assume now that A and B have entered into the following european option contract:

  • Put option,
  • Quantity = 10000,
  • Strike Price = $1200.

Again A took the long position and B - short. Below we present payoff charts for the possible Settlement Prices.

As we can observe, the payoff functions are nonlinear with respect to the Settlement Price which is in line with formula (#). What is more, the payoff function of the investor A (B) is non-increasing (non-decreasing). For put option it is explicable, as long (short) position should be less profitable, if Settlement Price increases (decreases).

Example - call option

Assume again that A and B took respectively long and short position in the following contract

  • Call option,
  • Quantity = 10000,
  • Strike Price = $8000,
  • Option Premium = 0.000003 BTC.

This time we add margining to our considerations. Since a long position in an option means that the payment function is nonnegative, therefore a margin for that option is constant and equal to Total Option Premium.

Margin (long) = Initial Margin = Total Option Premium = Option Premium * Quantity

This means that a long position holder in an option can never go bankrupt (nor receive a margin call on that position). In our case

Margin (A) = 0.03 BTC.

The case is different for B, who took the short position. The formula is as follows

Margin (short) = Max(Margin Percent - OTM Percent, 0.5 * Margin Percent) * 1 / Futures Mark Price * Quantity,

where

  • Margin Percent - 10% for Initial Margin and 8% for Maintenance Margin,
  • OTM Percent = (1 / Strike - 1 / Futures Mark Price) / (1 / Futures Mark Price),
  • Futures Mark Price - current Mark Price of the futures contract with the same maturity (see the article onfutures) denominated in BTC.

Therefore (assume current Futures Mark Price = 10,000):

Initial Margin (B) = Max(10% - 2%, 5%) * 1 / 10000 * 1000 = 0.08 BTC, Maintenance Margin (B) = Max(8% - 2%, 5%) * 1 / 10000 * 1000 = 0.06 BTC.

Notice that this means that OTM option sellers can utilise leverage up to 20x, in comparison with ATM or ITM short option position holders, who can trade with up to 10x leverage (before taking into account option delta).

So B has to keep up big enough deposit in order to not get bankrupt (since Futures Mark Price can raise with time). Assuming that it is the case we can calculate the outcome for both investors using the formula:

Settlement P\L = Side * Quantity * (Option Payoff - Option Premium).

Option Payoff depends clearly on the Settlement Price as in the chart below.

Log returns vs Payoff

Moneyness describes the relation between current spot price and strike price. We will define Log Returns as logarithm of moneyness that is

Log Returns = log( Spot Price / Strike Price ).

We are going to display the relation between payoff values and Log Returns. Assume investors A and B took long and short position respectively in european call option contract with parameters defined same as in the preceding example. The relation between payoff values and log moneyness in this specific situation is presented at the following chart.

The results are quite clear. In case of A (B), the higher (lower) the Settlement Price is, the higher (lower) Payoff is. In case of put option results are analogous. One can see that plotting option Payoff against Log Returns makes the dependence more "linear".